The question could be interpreted in two ways. How to determine if something is a mineral? Or, how to determine what a particular mineral is?

In order to classify something as a mineral, it must meet four characteristic criteria. A mineral is a naturally occurring, inorganic, and solid, with a crystal structure.

Naturally occurring means not man made. It must have been created through natural forces. That's why cubic zirconia diamonds are not classified as minerals.

Inorganic means the material is not part of a living creature and never was.

Solid means the mineral is not normally a liquid or gas. That one is fairly straightforward.

Crystal structure means that the atoms/molecules that make up the mineral are arranged in a regularly repeating geometric shape of some kind. Cubes for example.

In order to identify what a certain mineral is, you should examine characteristic properties of minerals. Those would be luster, hardness, color, streak, cleavage, fracture, and density. If your sample is a pure mineral sample, the best test to identify what mineral it is would be to use density. Each mineral has its own unique density. It's equivalent to a fingerprint.

I'm assuming that you are asking what the easiest way to identify a certain mineral is.

Identifying what mineral a certain mineral given to you is requires more than one step, as well as elimination.

Make sure that you have a good piece of the mineral that you will be studying. You want to make this easier, after all, so you'll want a nice chunk of it (or many small pieces)

Luster, or how the surface of the mineral reflects light, is the next step. You must determine if your mineral is metallic, glassy, or dull. This is a bit tricky sometimes, because some minerals don't seem to have a definite answer. Check the below URL for more help on that.

Hardness determination is next! Use the 10-point Mohs scale. You have to use several items with predetermined hardness ratings on Mohs scale, so you can eventually find out the hardness of your mineral with more elimination processes! When one substance rubs off of another, that means that the substance that rubbed itself off onto the other is softer. Check the below URL for a larger explanation.

Examine the color of your mineral. Be precise; being to vague will mislead you.

Streak color, which is more accurate than just the color that you examined in the previous step (because some residue that makes the mineral look discolored may occur). All you must do is take the mineral and scratch it along something rough, usually using a streak plate. Observe the color of the powder left behind.

Magnetism, which basically means if the mineral is magnetic, or attracted to magnets.

For the last resort tests, you can taste the mineral in case it is salty (not recommended), you can see if there's a reaction of the mineral with vinegar. You can also hold the mineral and determine if it has an unusual proportion/difference from the weight you expect it to be based on size or other factors, compared to the actual weight. This is called heft.